MEASUREMENT OF SOLIDS 
333 
the parallelepiped (1) is on A R as base and has height h ; the 
prism (2) is equal to a parallelepiped on KQ as base and with 
height h; the prism (3) is equal to a parallelepiped with JSP 
as base and height h\ and finally the pyramid (4) is equal to 
a parallelepiped of height h and one-third of RC as base. 
E H 
Therefore the whole solid is equal to one parallelepiped 
with height h and base equal to (AR+KQ + NP + RO + ^R0) 
or AO + ^RO. 
Now, if AB = a, BO = b, EF = c, FG = d, 
AV = |(a + c), AT = %(b + d),RQ = \(a — c), RP = ±(b — d). 
Therefore volume of solid 
= {\(a + c) {b + d)+-^i a — c ) {b — d)} h. 
The solid in question is evidently the true (3u>/j.l(tkos (‘little 
altar’), for the formula is used to calculate the content of 
a PcofjLicrKos in Stereom. II. 40 (68, Heib.) It is also, I think, 
the (7(f)T]VL(TK09 (‘ little wedge ’), a measurement of which is 
given in Stereom. I. 26 (25, Heib.) It is true that the second 
term of the first factor ^ (a — c) (b — d) is there neglected, 
perhaps because in the case taken (a — 7, b = 6, c = 5, d = 4) 
this term (— -|) is small compared with the other (= 30). A 
particular a-cfrrjvLa-Ko?, in which either c — a or d = b, was 
called 6w£; the second term in the factor of the content 
vanishes in this case, and, if e.g. c = a, the content is \(b + d)ah. 
Another f3oo/jLi(TK09 is measured in Stereom. I. 35 (34, Heib.), 
where the solid is inaccurately called ‘a pyramid oblong 
(trcpofirjKr]s) and truncated (KoXovpos) or half-perfect